I've had connections at SIN on *A airlines (different airline inbound and outbound) of an hour or less and made every one of them - although sweated a close call a couple of times.

The only problem will be if inbound is significantly delayed (more than an hour). As its separate tickets the airlines have no obligation to protect your continuing flight. What happens will depend on fare rules of the second ticket, your status with them, also how much of a delay and how many passengers affected (eg if you're the only ones and first flight is 2 hours late they probably wont hold the second flight, but if there are lots of connecting passengers on those flights and first flight is 80 minutes late they may well hold the second).

In situations like this I try to make the second ticket flexible enough to cope with missing the booked flight, and also a backup plan for what I'll do if miss it.